That chapter starts with Scout complaining about how their father isn't as interesting as other kids' fathers. He doesn't play sports with them and just seems too old to have fun with his kids. Being a widower, he devoted a lot of his efforts into providing for his children and raising them to be good people. They had no idea that their father was such a good shot, and were surprised by how accurate he was. For Scout, clearly her father is a little "cooler" by the end of the chapter, but it means so much more than that. It's a paradigm shift for the kids to see their father performing such a task.
It's not that Atticus was anti-gun; he does, after all, buy his children rifles, which is generally unheard of these days. Hunting was a normal thing for any man to do, so men (and women) of all backgrounds were likely to be able to shoot. It was simply that the deadly power of a gun was not the kind of power that Atticus preferred to be known for; rather, he wished to be known for his intellect and his kindness. Reading this incident from Scout's point of view allows us to see Atticus as a larger-than-life figure, a hero wielding a weapon for the cause of good. Then, when the reader sees Atticus in the trial and its aftermath, that heroic persona is complemented.
When Tim Johnson, a rabid dog walks down the Finch's street, Jem and Scout are surprised to find that Atticus can shoot with deadly accuracy. They later learn that as a young man his nickname was Ol' One Shot Finch.